Editing Discretization (section)

=== Discretization of process noise ===
Numerical evaluation of {{math|'''Q{{sub|d}}'''}} is a bit trickier due to the matrix exponential integral. It can, however, be computed by first constructing a matrix, and computing the exponential of it<ref>Charles Van Loan: ''Computing integrals involving the matrix exponential'', IEEE Transactions on Automatic Control. 23 (3): 395–404, 1978</ref>
<math display=block>\begin{align}
  \mathbf{F} &= \begin{bmatrix} 
    -\mathbf{A} & \mathbf{Q} \\
    \mathbf{0} & \mathbf{A}^\top 
  \end{bmatrix} T \\[2pt]
  \mathbf{G} &= e^\mathbf{F} = \begin{bmatrix} 
    \dots & \mathbf{A_d}^{-1}\mathbf{Q_d} \\
    \mathbf{0} & \mathbf{A_d}^\top
  \end{bmatrix}
\end{align}</math>
The discretized process noise is then evaluated by multiplying the transpose of the lower-right partition of {{math|'''G'''}} with the upper-right partition of {{math|'''G'''}}:
<math display=block>\mathbf{Q_d} = (\mathbf{A_d}^\top)^\top (\mathbf{A_d}^{-1}\mathbf{Q_d}) = \mathbf{A_d} (\mathbf{A_d}^{-1}\mathbf{Q_d}). </math>